1. Make the Pie Dough: Process the flour, salt and sugar in a food processor until combined. Add the shortening and process until the mixture has the texture of coarse sand, about 10 seconds. Scatter the butter pieces over the flour mixture; cut the butter into the flour until the mixture is pale yellow and resembles coarse crumbs, with butter bits no larger than small peas, about ten 1-second pulses. Turn the mixture into a medium bowl.
2. Sprinkle 8 tablespoons of the ice water over the mixture. With a rubber spatula, use a folding motion to mix. Press down on the dough with the broad side of the spatula until the dough sticks together, adding up to 2 tablespoons more ice water if the dough will not come together. Divide the dough into 2 balls, one slightly larger than the other. (If possible, weigh the pieces; they should weigh 16 ounces and 14 ounces.) Flatten the larger piece into a rough 5-inch square and the smaller piece into a 4-inch disk; wrap separately in plastic and refrigerate at least 1 hour, or up to 2 days, before rolling.
3. Remove the dough from the refrigerator (if refrigerated longer than 1 hour, let stand at room temperature until malleable). Roll the larger piece of dough to a 15x11-inch rectangle, about 1/8-inch thick; transfer the dough rectangle to a baking sheet lined with parchment paper. With a pizza wheel, fluted pastry wheel or paring knife, trim the long sides of the rectangle to make them straight, then cut the rectangle lengthwise into 8 equal strips.
4. Next, roll the smaller piece of dough on a lightly floured work surface to a 12-inch circle. Transfer the dough to a 9-inch pie plate. Working around the circumference of the pan, ease the dough into the pan corners by gently lifting the edge of the dough with one hand while pressing into the pan bottom with the other hand. Leave the dough that overhangs the lip of the pie plate in place. Place the baking sheet with the strips of dough in the freezer and the dough-lined pie plate in the refrigerator; chill for 30 minutes.
5. Make the Pie Filling: Meanwhile, adjust an oven rack to the lowest position, place a rimmed baking sheet on it and preheat the oven to 500 degrees.
6. In a small bowl, whisk together the sugar, cornstarch, cinnamon and salt; set aside. Place the cherries in a large bowl and stir in the almond extract. Sprinkle the sugar mixture over the cherries and using a rubber spatula, gently mix together until combined.